On topological Clifford semigroups embeddable into products of cones over topological groups

In this paper we give characterizations of topological Clifford semigroups which are embeddable into Tychonoff products of topological semilattices and cones over topological groups. Also we characterize topological Clifford semigroups which embed into compact topological Clifford semigroups.     

Derivation of the limit equations of elasticity theory on thin nets

A new approach is proposed to the study of plane problems of elasticity on rod junctures. This approach is based on so-called structural theorems and yields a fairly simple method of passing to the limit in the integral identity and thus obtaining the limit problem. In the case of nonlinear problems, the structural theorems make it possible to use variational methods like that of Γ-convergence of energy functionals. __________ Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 25, pp. 55–97, 2005.     

Numerical analysis of electromagnetic wave diffraction on a three-dimensional magnetodielectric body

A variant of the method of discrete sources suitable for solving problems of electromagnetic wave scattering on three-dimensional magnetodielectric bodies having a smooth surface of arbitrary shape is suggested and realized. A computer program implementing the suggested variant is briefly described. Some results of numerical calculations that illustrate the opportunities of the method are presented. Special attention is given to a study of the influence of deviations of the body shape from axisymmetric one on the bistatic scattering cross sections. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 50–57, October, 2005.     

On the Trotter-Kato theorem in a variable space

In this paper, the proof of a Trotter-Kato type theorem in a variable Banach space is given and some special cases and examples are considered.     

Averaging of Nonstationary Problems of Elasticity Theory on Thin Periodic Structures from the Point of View of Convergence of Hyperbolic Semigroups in a Variable Hilbert Space

In an abstract variable Hilbert space, the resolvent convergence of nonnegative self-adjoint operators is studied in the case where the limit of resolvents is a pseudoresolvent (the case characteristic for elasticity-theory problems on thin periodic structures). In particular, the resolvent convergence implies the convergence of semigroups and projection operators. On the basis of convergence of hyperbolic semigroups, the author obtains the averaging of the problems mentioned in the title of the paper, and, moreover, with various types of convergence: pointwise in time or in the mean in time. Moreover, the paper studies the spectrum of the limit operator of elasticity theory and the convergence to it of the spectrum of the initial operator of the corresponding stationary problem under its averaging. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 16, Partial Differential Equations, 2004.     

Homogenization of Problems of Elasticity Theory on Periodic Box and Rod Frames of Critical Thickness

A problem of elasticity theory in static statement on thin periodic box and rod frames whose geometry depends on two small parameters ɛ and h(ɛ) related to each other determining the cell of periodicity and thickness of the components (plates or rods, respectively) is studied. The homogenization of this problem is obtained in the most difficult case where . __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 12, Partial Differential Equations, 2004.     

Kinetics and Mechanism of Allyl Alcohol Epoxidation with Hydrogen Peroxide on a Titanium Silicalite Catalyst TS-1. Formulation and Discrimination between Hypothetical Mechanisms

Kinetics and Catalysis - The kinetics of epoxidation of allyl alcohol with hydrogen peroxide in the presence of a titanium-containing zeolite catalyst TS-1 has been studied. The hypothetical...